Interacting binaries typically have separations in the milli-arcsecond regime and hence it has been challenging to resolve them at any wavelength. However, recent advances in optical interferometry have improved our ability to discern the components in these systems and have now enabled the direct determination of physical parameters. We used the Navy Prototype Optical Interferometer to produce for the first time images resolving all three components in the well-known Algol triple system. Specifically, we have separated the tertiary component from the binary and simultaneously resolved the eclipsing binary pair, which represents the nearest and brightest eclipsing binary in the sky. We present revised orbital elements for the triple system, and we have rectified the 180-degree ambiguity in the position angle of Algol C. Our directly determined magnitude differences and masses for this triple star system are consistent with earlier light curve modelling results.